Rig Deformation: Mesh Deforms Badly When In Pose Mode - When No Pose Changes Have Been Made
It's because of the bone called DEF-chin.R (here in Rest Position):

you'll be able to see it if you enable its visibility in the armature layers:

You've given it a Damped Track and a Track To constraint with the bone called lips.R as Target, so as soon as you switch your armature to Pose Position it will point towards it:

When you parent a mesh it takes the armature Rest Position into account, and not its Pose Position, so when your armature switch to Pose Position, the bone will automatically move or rotate towards its target.
So you need to make sure that the position of this bone in Edit mode (i.e. their position in Rest Position) is the same position and rotation as in Pose mode, and reparent.
In Pose mode you can go in the header menu &gt; Pose &gt; Apply &gt; Apply Pose as Rest Pose. Make sure to duplicate your armature first so you can come back to a previous version.